Are People with Mental Illness Dangerous? A Bayesian Approach to Tackling Stigma

As part of the ongoing effort to stop Donald Trump from becoming the Republican Presidential nominee, an ad was circulated on Facebook recently featuring pictures of his wife Malania posing nude. The pictures were from a 2000 photo shoot with GQ, and the ad was produced by an anti-Trump “Super PAC” called Make America Awesome.

Although the Super PAC apparently has no ties to his principle rival in the Republican Primary, Senator Ted Cruz of Texas, Mr. Trump was quick to go on the offensive.

In response to the ad, Trump took to Twitter to warn Cruz to “be careful” or he would “spill the beans” on Cruz’s wife, Heidi. And although it’s unclear what exactly Trump was referring to, the New York Times noted one possibility – “a trying moment in her life and marriage in 2005, when she suffered through what Mr. Cruz has described as a ‘period of depression’ after moving to Texas from Washington to be closer to her husband.”

Was Trump threatening to “out” Heidi Cruz for having once struggled with depression? If so, this would be a particularly ugly move attempting to exploit public fears and misunderstandings about mental illness.

Mental Illness and Violent Behavior

As I’ve written before, mental illness is not at all uncommon. Each year, roughly 1 in 5 Americans are directly affected by some form of psychological disorder, whether it’s anxiety, depression, or schizophrenia, for example. Moreover, the average American has about a 50% chance of experiencing an episode of mental illness at some point during their lifetime.

Yet if mental illness is so common, why is there still such a pervasive stigma surrounding it?

There are likely a number of reasons for this. First, consider the language we use to describe people and behaviors we don’t like. Indeed, what message do we send to those struggling with serious mental illness when we casually and flippantly use words like “crazy” or “wacko” to insult or dismiss those we don’t like or those with whom we disagree?

But as much as words matter, there is another – likely more potent – reason for the lingering stigma surrounding mental illness. Many Americans believe people with mental illness are violent and unpredictable, no doubt partly because of the way mental illness is portrayed on television and in the movies.

Indeed, according to public opinion surveys, 60% of Americans think people with schizophrenia are likely to behave violently toward another person. Meanwhile, 32% of Americans think people with major depression are likely to do so.

In reality, the vast majority of people with mental illness are not violent. And according to recent research, the link between mental illness and violence is actually quite weak.

In a study published in the journal Law and Human Behavior, researchers analyzed crimes committed by people with mental illness and found that only 7.5% of offenses were directly linked to an individual’s symptoms. Among the 429 crimes that were analyzed, the researchers concluded that 3% of crimes were directly related to major depression, 4% were directly related to schizophrenia, and 10% were directly related to bipolar disorder. Moreover, the authors found no obvious pattern linking criminal behavior to mental illness. Two-thirds of the offenders who had committed a crime directly related to their mental illness had also committed earlier crimes for other reasons, such as poverty, unemployment, homelessness, or substance abuse.

So mental disorders are neither necessary, nor sufficient for violent behavior to occur. And when it comes to predicting violent behavior, the best predictors continue to be social, demographic, and economic factors, such as age and gender (most violent crimes are committed by young males), a history of violent behavior, early childhood exposure to violence, substance abuse, and stress caused by homelessness, unemployment, or divorce.

Okay, So Mental Illness Probably Doesn’t Cause Violence, But…

So, despite belief to the contrary, there is little scientific evidence suggesting mental illness directly causes violent tendencies.

But what about mental illness as an indirect cause of violence? After all, aren’t people with mental illness more likely than the rest of the general public to live in poverty and to abuse drugs and alcohol? And if this is true, then couldn’t a person with mental illness be more likely to commit a violent crime for no other reason than this?

To answer this question, it would be helpful if we could estimate the probability of someone committing a violent crime given that they are mentally ill. So let’s attempt to do exactly that, using a powerful mathematical tool called Bayes’ Theorem.

How Dangerous Are People With Mental Illness? A Bayesian Perspective.

A Primer on Bayes’ Theorem

Bayes’ Theorem describes a way to calculate the probability that an event will occur, based on observed evidence. For example, suppose you want to know how likely it is someone has cancer, but all you know about the person is their age. Using Bayes’ Theorem, we can incorporate information about age to formulate a more accurate and precise estimate of cancer risk, provided cancer and age are related.

For instance, let’s say we want to estimate the chances that an individual has cancer given that they are 70 years old.

To determine this, we just need to plug a few pieces of information into Bayes’ Theorem, which is shown below in a generic form:

Equation 1: Bayes’ Theorem

Bayes Theorem

But before we go ahead and start plugging in numbers, let’s unpack this a bit and define each of the key terms in the equation:

p(H1|E) = this is the posterior probability, and it is what we are trying to estimate. It is the conditional probability of your Hypothesis (H1) given the observed Evidence (E). In this example, it is the probability of having cancer given that an individual is 70 years old.

p(E|H1) = this is the conditional probability of the evidence (E) given your Hypothesis (H1). In this example, it is the probability of being 70 years old given that you have cancer. To put it another way, it is the proportion of all the people with cancer who are 70 years old.

p(H1) = this is the baseline probability (or prior probability) of your hypothesis. It is the probability of your Hypothesis (H1) regardless of the observed evidence. In this example, it is the probability of having cancer, regardless of age.

p(E|H2) = this is the conditional probability of the evidence (E) given some alternative hypothesis (H2). In this example, it is the probability of being 70 years old given that you do not have cancer. To put it another way, it is the proportion of all the people without cancer who are 70 years old.

p(H2) = this is the baseline probability of the alternative Hypothesis (H2). It is the probability of the alternative Hypothesis regardless of the observed evidence. In this example, it is the baseline probability of not having cancer, regardless of age.

Now let’s make up some numbers to demonstrate how this works.

Let’s pretend there is a 1% chance of having cancer and that 25% of people with cancer are 70 years old. Furthermore, let’s pretend only 15% of people without cancer are 70 years old. This gives us everything we need, as shown below (note that all percentages have been converted to probabilities):

p(H1) = p(cancer) = baseline probability of having cancer = 0.01

p(H2) = p(no cancer) = baseline probability of not having cancer = 0.99

p(E|H1) =p(70 years old|cancer) = probability that someone is 70 years old given that they have cancer = 0.25

p(E|H2) = p(70 years old|no cancer) = probability that someone is 70 years old given that they do not have cancer = 0.15

With this information, we can now solve for p(cancer|70 years old) – the probability of an individual having cancer given that he or she is 70 years old.

Substituting the numbers above for each of the terms in Equation 1 gives us the following:

Bayes Theorem Cancer Example

So in this hypothetical example, the chance of a 70 year-old individual having cancer is about 1.65%, which is just slightly higher than the baseline 1%. If you look once again at the numbers I made up for this example, this outcome makes perfect sense given that 70 year-olds are disproportionately represented among those with cancer – 25% of all cancer patients compared to only 15% of those in the rest of the general population.

Now let’s see how we can use Bayes Theorem to figure out just how much of a threat people with mental illness actually are to the rest of the general public.

Estimating the Probability of Violent Behavior among People with Mental Illness

Imagine you are on your way to a friend’s party, where you know you will be meeting your friend’s out-of-state cousin for the first time. You know absolutely nothing about your friend’s cousin, other than the fact that he or she has been diagnosed with some form of mental illness.

The question is this: what are the chances your friend’s cousin will commit a violent crime during any given year?

Just as in the example above, we can formulate an estimate using Bayes’ Theorem. Let’s begin by defining our terms and outlining some estimates:

p(H1|E) = p(violent|MI):

This is the conditional probability of committing a violent crime given the observed evidence of mental illness. Again, this is what we are trying to estimate.

p(H1) = p(violent):

This is the baseline probability of committing a violent crime regardless of the presence of mental illness. According to FBI records, approximately 0.4% of the U.S. population was arrested for committing violent crimes in 2014 (the most recent year for which data are available). Therefore, I’ve estimated the baseline probability of committing a violent crime to be around 0.004.1

p(H2) = p(not violent):

This is the baseline probability of not committing a violent crime, and it can be estimated as 1- p(violent) or 0.996.

p(E|H1) = p(MI|violent):

This is the conditional probability of the presence of mental illness given that a violent crime has been committed. In other words, it is the proportion of violent crimes committed by people with mental illness. Based on research suggesting about 18% of crimes are directly or mostly attributable to symptoms of mental illness, a reasonable estimate for this value is likely somewhere between 10-25%. Therefore, for this term, I’ve selected a range of values between 0.10 and 0.25.

p(E|H2) = p(MI|not violent):

This is the conditional probability of the presence of mental illness given that a violent crime has not been committed. In other words, it is the proportion of people without a violent criminal record who have mental illness. Based on research suggesting mental illness affects roughly 20% of the U.S. population in a given year, I’ve estimated this value at around 0.20.

So what is the probability someone will commit a violent crime given that they have a diagnosed mental illness?

Bayes Theorem Mental Illness and violence

Given the information described above, the answer is around half of 1% – specifically anywhere between 0.20% and 0.50%, depending on the value chosen for p(MI|violent) – the proportion of violent crimes committed by people with mental illness. Therefore, during any given year, about 5 out of every 1,000 people with mental illness are likely to commit a violent crime, compared to 4 out of every 1,000 people in the general population.

And just so you don’t think I’ve stacked the deck by selecting an especially low range of values for p(MI|violent), take a look at Figure 1, which shows the probability of committing a violent crime across a wide range of values for both p(MI|violent) – the proportion of violent crimes committed by people with mental illness – and p(violent) – the baseline probability of committing a violent crime regardless of the presence of mental illness.

Figure 1: Range of probabilities reflecting risk that an individual with mental illness will commit a violent crime during any given year.

mental illness violence risk
Note: p(violent|MI) = probability of committing a violent crime given the presence of mental illness; p(violent) = baseline probability of committing a violent crime regardless of mental illness; p(MI|violent) = probability of mental illness given that a violent crime has been committed; p(MI|not violent) = 0.20.

There are two important results to point out in Figure 1:

  1. Because mental illness is fairly prevalent in the general population (affecting roughly 20% of Americans in a given year), an individual’s risk of violence is rather low across a wide range of values for p(violent). In fact, the baseline probability of committing a violent crime in the general population would need to exceed at least 0.45 before an individual with mental illness posed a greater than 50% chance of committing a violent act. In other words, in order for someone with mental illness to pose a greater than 50% chance of committing a violent crime, nearly half of all people in the general public would need to a commit violent crime, as well! If the risk of violent crime in the general population were this high, we would clearly have more to worry about than any specific danger posed by a person with mental illness.
  2. Even if a large number of violent crimes were, in fact, committed by people with mental illness – for instance, even if p(MI|violent) was as high as 0.90 – the chance of an individual with mental illness committing a violent crime would still be quite low. This is because the baseline probability of violent crime in the general population is extremely low at 0.004. So, even if 90% of violent crimes were committed by the mentally ill, the risk of violent crime from any single individual with mental illness would still be only 1.8%.

Combatting the Stigma: Compassion ‘Trumps’ Fear

As research has shown – and as this statistical simulation is meant to show – the vast majority of people with mental illness are not dangerous. Other social, economic, and demographic factors – such as age, gender, poverty, childhood exposure to violence, and substance abuse – are far better predictors of violence than mental illness. Moreover, the risk of violent crime from any single individual with mental illness is extremely low, perhaps between 0.20 – 0.50%.

Yet unfortunately the stigma surrounding mental illness will persist without real, meaningful reform of the U.S. mental health system and without a conscious effort from each of us to stop trivializing mental illness and using outdated mental health labels to demean, dismiss, and insult others.

When we use words like “crazy” or “nut job” as intended insults, we send a powerful – albeit unspoken – message that people with mental illness are inferior and unworthy of empathy and compassion. And when we attempt to shame or embarrass others because of their struggles with mental illness, this message is only spoken more clearly and forcefully.

Which brings us back to the matter of Donald Trump.

On his official campaign website, Mr. Trump professes a desire to combat the stigma surrounding mental health so that more veterans and service members will choose to seek treatment for illnesses such as post-traumatic stress disorder (PTSD). However, as we are all now well aware, Mr. Trump relishes hurling personal insults at political rivals, and many of his favorite insults have an obvious mental health connotation – “crazy,” “basket case,” “wacko,” “nut job,” and “unstable,” for instance. By equating mental illness with personal weakness, low intelligence, and general inferiority, Mr. Trump perpetuates the very stigma he claims to want to put to rest.

This is important because there are real consequences to stigma. For instance, President George W. Bush’s New Freedom Commission on Mental Health concluded that stigma leads those in the general public to avoid socializing with, working with, and employing people with mental illness. It also leads people to be less empathetic and less willing to pay for mental health care. And on the side of those with mental illness, stigma leads to low self-esteem, isolation, and feelings of hopelessness. It also deters people from seeking the medical and therapeutic help they need.

Sadly, according to the National Alliance on Mental Illness (NAMI), nearly two-thirds of people with a diagnosed mental illness do not seek treatment. And those struggling with serious mental illness die, on average, 25 years earlier than those without mental illness, often because of treatable medical conditions.

Moreover, none of what I’ve said here is meant to suggest that people with mental illness are entirely unacquainted with violent and criminal acts. Quite the contrary. People with mental illness are up to ten times more likely to be victims of violent crime compared to the rest of the general population.

So make no mistake, even though most people with mental illness pose no danger at all to the general public, lives are endangered by mental illness nonetheless.

 

Footnotes:

[1] Note that I use the FBI’s definition of violent crime, which includes murder and nonnegligent manslaughter, forcible rape, robbery, and aggravated assault.

 

Brian Kurilla is a psychological scientist with a Ph.D. in cognitive psychology. You can follow Brian on Twitter @briankurilla 

 

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